Systems and methods for process modeling and analysis are well known in the art. For example, artificial neural networks, such as those disclosed in co-pending patent application, entitled “An Improved Method and System For Training An Artificial Neural Network,” having a filing date of Mar. 31, 1999, Ser. No. 09/282,392, and assigned to the same assignee as the present patent application, multi-variate state estimation techniques (MSET), as described by Singer, et al., in a paper entitled “Analytical Enhancements of Automotive Century System Reliability,” dated June 1994, and multiple regression techniques, all are used for process modeling and analysis in varying applications. Similarly, prior art basic nonlinear state estimation techniques are also known for use in process modeling. Each of these prior art methods, however, suffers from limitations in terms of accuracy and modeling flexibility.
Artificial neural networks, for example, although suitable for modeling certain systems, require extensive training and are time-intensive, which makes them unsuitable for applications in which a system, and corresponding modeling of that system, must be done in near real time. An artificial neural network would thus be unsuitable, for example, to predict behavior in a e-commerce setting where the future behavior of a customer is desired to be known. Applying artificial neural networks to model the behavior of each customer in such an application, in which new information (in the form of additional variables) becomes available as time evolves, is not possible, as means do not exist for rapid adjustment of the model of such a system to predict behavior. The iterative process required to train an artificial neural network is not conducive to modeling rapidly changing systems in which a rapid model adjustment is necessary once one or more new variables has become available.
MSETs and basic NSETs also face limitations in that they rely upon the inversion of data matrices (recognition matrices) that are sometimes singular (in which case inversion is impossible) or near-singular, in which case inversion is possible but end result prediction accuracy is negatively affected. Furthermore, MSETs have poor stability with respect to choice of data included in the prototype matrix, i.e., the inclusion/exclusion of any particular single data point in the prototype matrix can unduly affect prediction results. This is actually a result of co-linearities among the prototypical data points.
Lastly, the distance/similarity function typically chosen for use in MSETs is selected based upon its tendency to produce relatively well-conditioned (when compared to other distance/similarity functions) recognition matrices. Condition is an inverse measure of singularity (i.e., well-conditioned implies non-singular, which is good, while poorly-conditioned implies near-singular, which is bad). Such a distance/similarity function, while generally providing better-conditioned recognition matrices, is not optimal in terms of accuracy and modeling flexibility.